School of Science - Department of Mathematics

0301712Functional Analysis

• Course Description :Hilbert spaces: the geometry of Hilbert space, the Riesz  representation theorem, orthonormal bases, isomorphic Hilbert  spaces, operators on Hilbert space: basic properties and examples, adjoints, projections, invariant and reducing  subspaces, positive operators and the polar decomposition, self-adjoint operators, normal operators,  isometric and unitary operators, the spectrum and the numerical range of an operator, operator inequalities, compact operators, Banach spaces: basic properties and examples, convex sets, subspaces and quotient spaces, linear functionals and the dual spaces, the Hahn-Banach theorem, the uniform boundedness principle, the open mapping theorem, and the closed graph theorem.
• Pre Request : 0301711
• Credit Hour :3
• Department : Mathematics
• Program :
• Course Level :Master
• Course Outline :

  0301712 Syllabus.pdf